E209 - Maths - week 8 Calculations (chapter 15 - FRACTIONS (ref from…
E209 - Maths - week 8 Calculations
we are normally good enough for everyday maths- estimations ok in real life.
what do you picture in your head.?
(trafalgar sq not what think if associated with maths!)
diagonal or half straight? not ambiguity!?
maths symbols limit redundancy
stressing and Ignoring
video resources for Block 2 Julie Greer, the head teacher at Cherbourg primary school, referred to supporting children ‘towards mastery’ and Mark Edgeller, the maths coordinator, said that the school is looking very closely at initiatives in schools within the UK that focus on ‘mastery’, drawing on approaches used in Shanghai and Singapore.*
Scottish gov talk of S. Asia
Children learning techniques
Askew, 2016, p. 64 questions whether it's about getting the correct answer or getting to grips with maths
calculation stratagies particularly strong - same explanations !
same for - 3 Fractions, decimals, percentages, ratio and proportion
apart from 'mixed number' (eg 1 3/4)
and Different representations! -apart from clumsy mistake for ratio (said 1:8 not 1:7)
factor = opposite of multiple! its the numbers that multiply within it
product is specifically multiplication answer
difference is subtraction specific answer
quotient = division answer
correct- sum= addition answer (and is addition specific!!!)
One of the reasons many children experience difficulties with this area of mathematics is that these five connected ideas are often taught separately. Decimals can be particularly challenging for some children due to the place-value element. Helping children to make links between the different representations can be very beneficial to their understanding. It also helps them ‘see mathematics as a whole rather than a series of separate and often disparate ideas’ (Cotton, 2016, p. 6)
eg- 1/8 as a decimal. what is 1/4 as percentage, so what is 1/8 so if 12.5% what is that as a decimal
activity 8.1 comment
Activity 8.2 - I gave same example of using a pizza as a mental image...so much simpler
reader chapter 7
he reckons 2 types of addition - AGGREGATION & AUGMENTATION.p.88-90
4 types of subtraction
how many left? How many are not..?
start at, reduce by, go down
what is difference? How many more/less?
inverse of addition
how many more needed
I think you can word the same calculation as any of them!! nonsense!! eg inverse is a form of comparison !!
Nesher & Teubel (1975) c Hay/Man p.100 - Isreal study if wording sounding addition kids got confused.
reader chapter 8
algorithm- the way to do a calculation- tried and tested technique (p52)
p.105- write horizontally until capable. vertical algorithms can cause confusion
in box p105- many ways of getting correct answer. informal mental just as valid if get correct answer !!!
p115- to be able to encourage children staff must be familiar and confident in using informal strategies and formal algorithms!!!
p.106- have to be able to count forwards and backwards in 10s- eg 7, 17,27, 37... - needs specific teaching and frequent reinforcement
number lines and stepping stones
mentally we work left-right but written algorithms are usually R-L.
COMPENSATION- good technique (eg 140-99= 140-100+1)
make 'friendly' numbers
rounding up and down to make estimates
use this technique to estimate answer- can easily make an error in algorithm or on calculator p.113
children are good with multiples of 5 (cos of fingers?) p.111
Belgium & OZ examples - p.114
Haylock and Manning (2014) – that calculating mentally should not mean that children do not write anything.
jot workings out etc
chapter 9 -WRITTEN CALCULATIONS
work R-L instead
once understand principal can add larger numbers and multiple numbers - p.121
coins good starting point to explain 'carry one over'
subtraction by DECOMPOSITION
is taught nowadays inline with
learning maths with understanding
p.123 (equal additions is by rote)
key is understanding of place value
EXCHANGE / EXCHANGING 1 10 for 10 1s
equal addition mean adding 10 to both numbers - the difference between our heights same if both stood on a table!! 'borrow one & pay it back" just something you'd say.
CONSTANT DIFFERENCE METHOD
has elements of equal additions- add 3 to both or add 50 to both to make easier numbers
common mistakes when there is a zero digit!! p.131
we still sometimes say 'borrow' when should be 'exchange'
P.130 - always CHECK subtraction by doing an addition !
writing out in full and working L-R is most logical !! eg 200 + 50+ 7 plus 500+70+6 equals 700 + 120 + 13 = 833
chapter 15 - FRACTIONS
remainder can be displayed as a fraction too. but depends on context if appropriate. choc bars-yes, vans -no p.213
cancelling= simplify fractions- to lowest denominator p.211
adding or subtracting FR not v common- usually use decimals. but have to be able to do it- p214
multiplying simple fractions - is vital basic step to prepare for secondary school when
'manipulating algebraic expressions and simplifying formulas'
p.215 nice visual of shaded box 2/3 of 3/4- many won't get that!!!
'of' = multiplication p.216
p.217 Haylock and M appreciate fractions good prep for algebra but because nowadays metric and decimals they say mostly still used due to
...duh - you just said preparation for algebra!!!
number line helpful p.218
division of fraction is inverse of multiplication. image of pizza makes 20/ 1/4 easy p.219
ref from Boulet, 1998 study?? p.219
as highlighted by
easier if same amount of digits after decimal point...add the zeros if necessary
kids do not need to know the technical terms just the concepts ! online review of H&M
good for TMA - WP girls jump straight to a written algorithm when sometimes mental is better